Intuitionistic fuzzy information measures with applications in decision making processes

Abstract

Entropy was introduced by Shannon to measure uncertainty, which considered only statistical processes and was the average rate at which information being produced by a stochastic source of data. Since the inception of fuzzy sets given by Zadeh, uncertainty arises due to partial information or imprecise information has been measured. Thus fuzzy entropy has become an effective tool in dealing with real life situations pertaining to disciplines such as civil engineering, medicine, pattern recognition, image processing, decision making etc. The generalized version of fuzzy sets has been introduced by Atanassov, known as intuitionistic fuzzy sets (IFSs), which have wide applications in decision making processes and consider both membership and non-membership functions. Other than IFSs, more generalized fuzzy sets like fuzzy soft sets, intuitionistic fuzzy soft sets etc. are also used for the purpose of decision making. Entropy is a measure of uncertainty and when this concept is flavored with generalized fuzzy set theory, it provides strong logical reasoning to handle real life situations and thus gives birth to new discipline as fuzzy information theory. For decision making purposes, many fuzzy information measures have been proposed by the researchers by using various mathematical functions that has given promising results. The biggest challenge is to select the suitable entropy for a particular situation. To overcome this, a new intuitionistic fuzzy information measure based on trigonometric function has been proposed in this work which has applications in decision making pertaining to disciplines like pattern recognition, image processing, medical diagnosis etc. Generalized fuzzy based decision making methods with the proposed entropy has been used for the purpose of decision making. Divergence is a measure of comparison between two objects. In this thesis, a new intuitionistic fuzzy divergence information measure has been proposed, which has application in real life situations. These proposed measures satisfies a